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This paper considered the transient drainage of a linearly viscous magnetohydrodynamic (MHD) fluid down a vertical flat slippery belt. An inhomogeneous partial differential equation with an inhomogeneous boundary condition was developed. Exact solutions for the velocity distribution, flow rate, surface profile, and variable thickness were then computed. The effect of MHD and the slip parameter on the velocity, flow rate, and surface profile were then considered. The effect of the magnetic field on the derived flow properties was discussed and represented graphically. It was determined that the absence of the magnetic field and the assumption of no-slip boundary conditions reduced the problem to the well-known Jeffreys problem. Key words: thin film flow, linearly viscous fluid model, MHD, exact solutions, transient drainage, slippery belt. Nous etudions ici le drainage transitoire d'un fluide MHD a viscosite lineaire, descendant sur une courroie verticale, plate et glissante. Afin de le decrire, nous developpons une equation differentielle aux derivees partielles inhomogene avec une condition limite inhomogene. Nous calculons des solutions exactes pour la distribution de vitesse, le taux d'ecoulement, le profil de surface et l'epaisseur variable. Nous considerons alors l'effet du caractere MHD et du parametre de glissement sur la vitesse, le taux d'ecoulement et le profil de surface. Nous discutons l'effet d'un champ magnetique sur les proprietes d'ecoulement et representons cet effet graphiquement. Nous determinons ensuite, qu'en l'absence de champ magnetique et sans condition limite de glissement, le probleme se reduit au probleme bien connu de Jeffreys. [Traduit par la Redaction] Mots-cles: ecoulement d'un film mince, modele de fluide a viscosite lineaire, MHD, solutions exactes, drainage transitoire, courroie glissante. PACS Nos.: 01, 47, 02.30., 1. Introduction The flow of fluid in the form of thin layers is called thin-film flow. A thin film consists of an expanse of liquid bounded by a solid body [...]

The multi-mode Richtmyer-Meshkov instability is numerically simulated by the large-eddy simulation code MVFT (multi-viscous-flow and turbulence). The Vreman, dynamic Smagorinsky, and stretched-vortex models are used to model the subgrid-scale flux of turbulence transport in simulations. The calculated widths of turbulent mixing zones are all in good agreement with the experimental results, and there is a little difference among the different SGS models. However, the decay factors of turbulent kinetic energy differ significantly for different SGS models, with relative error up to about 50%. It is concluded that the dynamic Smagorinsky model and stretched-vortex model can both predict the energy backscatter, with the prediction of the former weaker, while after reshock, the dynamic Smagorinsky model is absolutely as dissipative as the Vreman model. PACS Nos.: 47.40.Nm, 47.20.Ma. Nous simulons numeriquement l'instabilite multi-modes de Ritchmyer-Meshkov a l'aide du programme de simulation a larges tourbillons MVFT (multi-viscous-flow and turbulence). Nous utilisons les modeles de Vreman, de Smagorinsky et du vortex etire pour modeliser le flux d'echelle inferieure a la maille en simulations de transport turbulent. Les largeurs calculees des zones de melange turbulent sont tous en bon accord avec les resultats experimentaux et il y a une petite difference entre les differents modeles SGS. Cependant, les facteurs de decroissance de l'energie cinetique turbulente different de facon significative entre les modeles SGS, avec une erreur relative de 50%. Nous concluons que le modele dynamique de Smagorinsky et le modele du vortex etire peuvent tous les deux predire l'energie de diffusion arriere, la prediction du premier etant plus faible, alors qu'apres le deuxieme choc, le modele dynamique de Smagirinsky est tout aussi dissipatif que le modele de Vreman. [Traduit par le Redaction], 1. Introduction When impulsively accelerated by a shock wave, the perturbed material interface separating two different fluids will grow and eventually evolve into turbulent mixing. This phenomenon is known as [...]

Oedometer tests were conducted on dry and saturated kaolinite clay samples to investigate the effects of stress level, stress history, pore fluid type, and drainage path on time-dependent deformation under one-dimensional (1D) constant stress. Different deformation modes involved in the creep compression were identified and quantified: creep deformation of individual particles and creep shear displacement at particle contacts. It was found that the creep compression is a coupled process involving the above creep deformations and induced viscous flow resulting in pore compression. The rate of 1D creep compression is controlled by the drainage path along which the viscous flow occurs. It was also observed that mechanically induced consolidation has an accelerating effect on the creep compression of the test samples existing within the limit time zone. This observation confirms that 1D creep compression is a continuation of 1D consolidation in which the largest existing interaggregate pores collapse under a given effective stress. No creep compression was observed when the test samples were mechanically overconsolidated to a state beyond the limit time zone because the interaggregates were compressed to a stable structure. Reduced creep compression was detected in chemically induced consolidated samples though their states were beyond the limit time line. Key words: creep deformation, viscous behaviour, overconsolidation, chemically induced consolidation. Des essais a l'odometre ont ete realises sur des echantillons d'argile kaolinite secs et satures afin d'etudier les effets du niveau des contraintes, de l'historique des contraintes, du type de fluide interstitiel et du cheminement des contraintes sur la deformation dependante du temps sous une contrainte constante en une dimension (1D). Differents modes de deformation impliques dans la compression en fluage ont ete identifies et quantifies: la deformation en fluage de particules individuelles, et le deplacement en cisaillement en fluage aux points de contact entre les particules. Il a ete demontre que la compression en fluage est un processus couple impliquant les deformations en fluage mentionnees precedemment et l'ecoulement visqueux induit par la compression des pores. Le taux de compression en fluage 1D est controle par le chemin de drainage le long duquel l'ecoulement visqueux se produit. Il a aussi ete observe que la consolidation induite mecaniquement provoque un effet d'acceleration sur la compression en fluage des echantillons a l'interieur d'une periode de temps. Cette observation confirme que la compression en fluage 1D est une continuation de la consolidation 1D durant laquelle les plus grands pores interagreges existants s'effondrent sous une contrainte effective donnee. Aucune compression en fluage n'a ete observee lorsque les echantillons etaient surconsolides mecaniquement a un etat en dehors de la periode de temps limite, puisque les pores interagreges ont ete comprimes jusqu'a l'obtention d'une structure stable. Des compressions en fluage reduites ont ete detectees dans les echantillons consolides chimiquement malgre que leur etat etait au-dela de la ligne de limite de temps. [Traduit par la Redaction] Mots-cles: deformation en fluage, comportement visqueux, surconsolidation, consolidation induite chimiquement., Introduction The time-dependency on the volume change of clay observed in one-dimensional (1D) compression has been an active research area for decades. For practical applications, the volume changes over time [...]

For polymers with long, complicated, branched chains, it is difficult to measure the real shear viscosity and slip velocity, using the capillary rheometer based on the adsorption-desorption mechanism. In this study, a double-barrel capillary rheometer was used to investigate the viscosities of four polymers including polypropylene, high-density polyethylene, polystyrene, and polymethylmethacrylate in a microchannel. A general model of polymer viscosity based on the entanglement-disentanglement was presented. The proposed model is important in understanding the mechanism of wall slip. This general model can be transferred to the other different models when changing the parameters. Actually, the entanglement-disentanglement model can also be transformed to the adsorption-desorption model. Using the model, it was found that the viscosities of polystyrene and polymethylmethacrylate were reduced with decreasing die diameter, and the slip velocities were increased with the increase of shear stress which agrees well with polymer microrheology based on the microscale effect. For polymers with long, complicated, branched chains, the proposed model improves the accuracy of the calculated viscosity and gains the real slip velocity when polymer melt flows through a microchannel. POLYM. ENG. SCI., 52:1806-1814, 2012. © 2012 Society of Plastics Engineers, INTRODUCTION The benefits of plastics, such as mass production capability, disposability, and biocompatibility, make plastics the best choice for numerous medical and optical devices. Currently, many plastic products with microstructures [...]

Assuming that the background geometry is filled with a free gas consisting of matter and radiation and that no phase transitions are occurring in the early universe, we discuss the thermodynamics of this closed system using classical approaches. We find that essential cosmological quantities, such as the Hubble parameter H, scale factor a, and curvature parameter k, can be derived from this simple model. On one hand, it obeys the laws of thermodynamics entirely. On the other hand, the results are compatible with the Friedmann-Lemaitre-Robertson-Walker model and the Einstein field equations. The inclusion of a finite bulk viscosity coefficient derives important changes in all of these cosmological quantities. The thermodynamics of the viscous universe is studied and a conservation law is found. Accordingly, our picture of the evolution of the early universe and its astrophysical consequences seems to be the subject of radical revision. We find that the parameter k, for instance, strongly depends on the thermodynamics of the background matter. The time scale, at which a negative curvature might take place, depends on the relation between the matter content and the total energy. Using quantum and statistical approaches, we assume that the size of the universe is given by the volume occupied by one particle and one photon. Different types of interactions between matter and photon are taken into account. In this quantum treatment, expressions for H and a are also introduced. Therefore, the expansion of the universe turns out to be accessible. PACS Nos: 04.20.-q, 05.20.-y, 98.80.Cq Acceptant que le fond geometrique soit rempli d'un gaz libre compose de matiere et de radiation et qu'aucune transition de phase ne se soit produite dans l'univers naissant, nous discutons la thermodynamique de ce systeme ferme dans une approche classique. Ce modele simple permet d'obtenir des parametres cosmologiques essentiels, comme le parametre de Hubble H, le facteur d' echelle a et le parametre de courbure k.D' un cote, il obeit entierement aux lois de la thermodynamique, alors que de l' autre, les resultats sont compatibles avec le modele de Friedmann-Lemaitre-Robertson-Walker et avec les equations d'Einstein. L'introduction d'un coefficient de viscosite volumique non nul modifie significativement la valeur de ces parametres cosmologiques. Nous etudions la thermodynamique des univers visqueux et nous trouvons une loi de conservation. Consequemment, notre image de l'evolution de l'univers naissant et ses consequences astrophysiques semblent devoir etre revues de facon radicale. Par exemple, nous trouvons que le parametre de courbure depend fortement de la thermodynamique de la matiere du fond. L' echelle de temps, a laquelle une courbure negative peut apparaitre, depend de la relation entre le contenu materiel de l'univers et son energie totale. Utilisant une approche quantique et statistique, nous supposons que la grandeur de l'univers est le volume occupe par une particule et un photon. Nous tenons compte de differents types d'interaction entre particules et photons. Des expressions pour H et a sont introduites dans ce traitement quantique et il devient possible d'y etudier l'expansion de l'univers., 1. Introduction The equations of state (EoS) describing the matter and (or) radiation filling the cosmological background geometry play an essential role in determining the time evolution of the universe. [...]

A new approach to allow the modelling of the viscous behaviour of natural clay soils, including creep, stress relaxation and the effects of applied strain rate on soil stiffness, has been developed based on the BRICK constitutive model (published by Simpson in 1992). The new model, 'strain rate-dependent' (SRD) BRICK, was used in a series of simulations to demonstrate its capabilities in predicting realistic behaviour during one-dimensional compression and undrained triaxial tests in which applied strain rates were varied. Triaxial stress path tests conducted by Gasparre et al. in 2007 to assess the influence of creep, resulting from recent stress history, on soil stiffness were also simulated. The observed trends concerning the stiffness at small strains were successfully modelled. Key words: Constitutive modelling, stress history, clay, viscoplastic, BRICK, strain. Une nouvelle approche permettant de modeliser le comportement visqueux de sols argileux naturels, incluant le fluage, le relachement des contraintes et les effets du taux de deformation applique sur la rigidite du sol, a ete developpee a partir du modele constitutif BRICK (publie par Simpson en 1992). Le nouveau modele, appele << dependant du taux de deformation >> (SRD) BRICK, a ete utilise dans une serie de simulations pour demontrer ses capacites a predire le comportement realiste durant la compression unidimensionnelle et les essais triaxiaux non draines dans lesquels les taux de deformation appliques sont variables. Les cheminements des contraintes des essais triaxiaux realises par Gasparre et al. en 2007, utilises pour evaluer l'influence du fluage resultant de l'historique des contraintes recentes sur la rigidite du sol, ont ete simules. Les tendances observees en lien avec la rigidite a faibles deformations ont ete modelisees avec succes. Mots-cles : modelisation constitutive, historique des contraintes, argile, viscoplastique, BRICK, deformation. [Traduit par la Redaction], Introduction Accurate predictions of ground displacements are essential for the success of complex construction projects in crowded urban environments, where existing structures must be safeguarded from the impact of new [...]

Viscous polymer flow in embossing stage during thermal nanoimprint lithography was investigated. Flow behavior of the thermoplastic polymer was analyzed numerically and experimentally. Fixed grid scheme along with the finite element method was used for numerical analysis. Effects of process parameters such as the temperature, the stamp speed, and the stamp geometry on the filling pattern for single cavity were studied. Also the patterns with several cavities were analyzed to understand the flow behavior between adjacent cavities. Experiments were performed using PMMA sheets to confirm the effects of parameters obtained from numerical analyses. Two different types of geometries were considered and the filled patterns were observed using a scanning electron microscopy. Numerical results exhibited a similar tendency as the experimental observation. POLYM. ENG. SCI., 51:209-217, 2011. [C]2010 Society of Plastics Engineers, INTRODUCTION Nanoimprinting lithography (NIL) is a newly emerging technology for fabrication of micro/nano structures with simple equipment. While conventional photolitho-graphic approaches make pattern transfer through the use of photons or [...]

Particle collisions with the walls are very important in understanding the fluid-particle behavior near the walls and determining the boundary conditions of the particulate phases in two-fluid models. In this paper, we examine the velocity characteristics of several types of particles near solid walls by applying a resolved discrete particle method (RDPM), which also uses the immersed boundary approach to model the solid particles. We assume that the particles are spherical with an initial velocity that is prescribed. The particles are allowed to traverse part of the viscous fluid until they collide with the solid wall. The collision force on the particle is modeled by a soft-sphere collision scheme with a linear spring-dashpot system. The hydrodynamic force on the particle is solved directly from the RDPM. By following the trajectories of several particles, we investigate the effect of the collision model parameters to the dynamics of particle close to the wall. We report here the rebound velocity of the particle, the coefficient of restitution, and the particle slip velocity at the wall as functions of the collision parameters. [DOI: 10.1115/1.4002432]

In the present work, the Jeffery--Hamel flow problem has been studied using both first-and second-order velocity-slip models, and then compared with the no-slip model. The objectives are to observe the behavior of the flow predicted by the two slip models and to establish criteria for using the two velocity-slip models. The study concentrates on examining the effect of the change in the Knudsen number (Kn) on the velocity profiles, magnitude of slip at the wall, and skin friction coefficient. Assuming that a difference between the two slip models of the order of 10% or less justifies the use of the simple first-order model, the transitional Kn numbers have been found. These Kn numbers depend on the flow direction, being either inflow or outflow. Also, there are three distinct regions that specify where to use each of the no-slip, first-order, and second-order slip models. Further, the reversal of the flow has been investigated as a function of the Kn number and for different Re. a, where Re is Reynolds number and a is the wall angle. Using the second-order slip models, it is found that as the Kn number increases, reversal occurs at Re. a smaller than the 10.31 value at which flow reversal happens in the no-slip model, and increasing the Kn number leads to a reduction in the skin friction coefficient in all cases except when reversal occurs. [DOI: 10.1115/1.4000918]

The present study is concerned with the numerical simulation of free-surface wave flows around surface-piercing cylindrical structures using an unstructured grid-based unsteady Reynolds-averaged Navier--Stokes method. The volume of fluid method is implemented with a highly accurate scheme for flux evaluation on cell faces. The computational results are validated against existing experimental data that involve free-surface waves around surface-piercing structures, spilling breaking waves, bubbly free-surface in separated regions, and interaction between free-surface waves and underlying viscous flow. The validation results suggest that the present computational approach provides a tool that is flexible and accurate enough to capture the fundamental characteristics of flow physics associated with the unsteady free-surface wave flows around surface-piercing cylindrical structures. DOI: 10.1061/(ASCE)0733-950X(2009) 135:4(135) CE Database subject headings: Surface waves; Water flows; Cylinders; Piers.

This paper describes a new efficient automatic remeshing method for three-dimensional hybrid meshes for viscous flow simulations to accommodate the meshes with changes of small devices quickly and easily. This remeshing method has two notable advantages. First, hybrid meshes can be generated automatically from a baseline mesh when the small devices are moved and/or deformed. This enables shape optimization techniques to find better models quickly, because tens or hundreds of meshes are usually required during the process. Second, the updated hybrid meshes are the same as the baseline mesh except for elements around the small devices. Their effect can be evaluated more accurately. Solution data from the baseline mesh can be shared with new hybrid meshes (e.g., as an initial condition to expedite the convergence of computational simulations). The remeshing method is applied to the Japan Aerospace Exploration Agency's high-lift-configuration standard model with a nacelle chine in different locations to demonstrate its capability. Computational simulations are also performed to further discuss the effectiveness of the remeshing method.

Numerical modeling is employed to study the heat transfer modulation between the thermal protection shield and the gas flow that is caused by ejection of underexpanded pyrolysis gases through the cracks in the thermal protection shield. The simulations are performed for an axisymmetric bluff body flying at Mach 7. The influence of the geometry of the thermal protection shield on the heat transfer pattern is studied for two representative shapes. The results are presented for three different flight altitudes (low, ground level; moderate, 20 km; and high, 30 km). At the low altitude, the plume pressure is lower than the pressure behind the detached front shock wave and the plume propagates slowly along the wall surface. At high and moderate altitudes, the plume path (and, consequently, the convective heat transfer between the thermal protection shield and the plume) depends on the plume interaction with the bow shock wave. The effect of viscosity for the plume injection conditions and freestream Mach number considered is found to be negligible at simulated altitudes. The effect of the initial pressure of pyrolysis gas on the plume dynamics is significant. The presence of the blast wave associated with the underexpanded plume alters the heat transfer and increases mixing. Finally, the enhanced heat transfer caused by the emergence of multiple plumes is investigated.

For a massless fluid ([rho]=0), the steady flow along a duct is governed exclusively by viscous losses. In this paper, we show that the velocity profile obtained in this limit can be used to calculate the pressure drop up to the first order in [rho]. This method has been applied to the particular case of a duct, defined by two plane-parallel discs. For this case, the first-order approximation results in a simple analytical solution which has been favorably checked against numerical simulations. Finally, an experiment has been carried out with water flowing between the discs. The experimental results show good agreement with the approximate solution.

This paper presents a numerical study of the dynamic self-assembly of neutrally buoyant particles rotating in a plane in a viscous fluid. The particles experience simultaneously a magnetic torque that drives their individual spinning motion, a magnetic attraction toward the center of the domain, and flow-induced interactions. A hydrodynamic repulsion balances the centripetal attraction of the magnetized particles and leads to the formation of an aggregate of several particles that rotates with a precession velocity related to the inter-particle distance. This dynamic self-assembly is stable (but not stationary) and the morphology depends on the number of particles. The repulsion force between the particles is shown to be the result of the secondary flow generated by each particle at low but nonzero Reynolds number. Comparisons are made with analogous experiments of spinning disks at a liquid-air interface, where it is found that the variation in the characteristic scales of the aggregate with the rotation rate of individual particles are consistent with the numerical results. [DOI: 10.1115/1.2436587] Keywords: magnetic particles, rotating aggregate, hydrodynamic interactions, direct simulation

The forced convection in the thermal entrance region of a circular duct is analyzed by taking into account the effect of viscous dissipation. The results of the adiabatic-wall preparation are an initial temperature profile which, due to the viscous heating effect, is not uniform.

In this work, I present the form of the Navier-Stokes equations implied by the Helmholtz decomposition in which the relation of the irrotational and rotational velocity fields is made explicit. The idea of self-equilibration of irrotational viscous stresses is introduced. The decomposition is constructed by first selecting the irrotational flow compatible with the flow boundaries and other prescribed conditions. The rotational component of velocity is then the difference between the solution of the Navier-Stokes equations and the selected irrotational flow. To satisfy the boundary conditions, the irrotational field is required, and it depends on the viscosity. Five unknown fields are determined by the decomposed form of the Navier-Stokes equations for an incompressible fluid: the rotational component of velocity, the pressure, and the harmonic potential. These five fields may be readily identified in analytic solutions available in the literature. It is clear from these exact solutions that potential flow of a viscous fluid is required to satisfy prescribed conditions, like the no-slip condition at the boundary of a solid or continuity conditions across a two-fluid boundary. It can be said that equations governing the Helmholtz decomposition describe the modification of irrotational flow due to vorticity, but the analysis shows the two fields are coupled and cannot be completely determined independently. potential flow | vorticity I Navier-Stokes | self-equilibration | dissipation

The steady-state solutions of a strongly exothermic reaction of a viscous combustible material are examined in a channel filled with a saturated porous medium under Arrhenius kinetics, neglecting reactant consumption. The Brinkman model is applied and analytical solutions are fabricated for the governing nonlinear boundary-value problem.

The conventional velocity autocorrelation function expression for the temperature and density dependent self-diffusion constant D(T,rho) is reformulated to emphasize the way in which the initial particle momentum biases final mean displacement. The self-diffusion and viscous flow processes in terms of configuration space inherent structures and kinetic transitions between their basins are analyzed and one possible mechanism for this violation is found to emerge.

The method of lattice Boltzmann equation (LBE) is a kinetic-based approach for fluid flow computations. This method has been successfully applied to the multi-phase and multi-component flows. To extend the application of LBE to high Reynolds number incompressible flows, some critical issues need to be addressed, noticeably flexible spatial resolution, boundary treatments for curved solid wall, dispersion and mode of relaxation, and turbulence model. Recent developments in these aspects are highlighted in this paper. These efforts include the study of force evaluation methods, the development of multi-block methods which provide a means to satisfy different resolution requirement in the near wall region and the far field and reduce the memory requirement and computational time, the progress in constructing the second-order boundary condition for curved solid wall, and the analyses of the single-relaxation-time and multiple-relaxation-time models in LBE. These efforts have lead to successful applications of the LBE method to the simulation of incompressible laminar flows and demonstrated the potential of applying the LBE method to higher Reynolds flows. The progress in developing thermal and compressible LBE models and the applications of LBE method in multi-phase flows, multi-component flows, particulate suspensions, turbulent flow, and micro-flows are reviewed. Keywords: Lattice Boltzmann equation; Force evaluation; Grid refinement; Multi-block; Boundary condition; Single-relaxation-time; Multi-relaxation-time

Recent advances are presented in the development, implementation, and application of a novel solution adaptive method, the multiresolution (MR) scheme. The MR method uses the difference in information between adjacent grid levels on a set of nested grids for determining active and inactive grid cells. This amounts to computing the wavelet decomposition of the solution, which is known to be a rich source of regularity information. Shocks, contact discontinuities, reaction fronts, or any other inviscid and viscous flow features are identified and tracked in a time-accurate fashion. In active regions, the underlying finite volume scheme is solved in the usual manner, whereas in smooth regions, an inexpensive interpolation of the numerical divergence replaces both flux computations and reconstruction. Thus, the simulation becomes significantly more efficient without any loss of accuracy compared to the finest grid available. The combined finite volume-MR method will be described followed by two-dimensional and three-dimensional time-accurate examples on unstructured meshes.

Aerodynamic augmentation in the presence of a thin high-temperature onboard plasma jet directed upstream of a slightly blunted cone was studied experimentally and numerically. The flow around a truncated cone cylinder at zero incidence was considered for Mach numbers [M.sub.[infinity]] = 2.0, 2.5, and 4.0. For the first time, computationally validated experimental pressure distributions over the model surface in the presence of the plasma jet were obtained. As in the conventional (nonplasma) counterflow jet, two stable operational regimes of the plasma jet were found. These were a short penetration mode and a long penetration mode (LPM) aerospike into the opposing supersonic freestream. The greatest drag reduction occurred in the moderate LPM regime. LPM strong overblowing reduces the benefits. The experimental pressure results were approximately validated against an Euler computational fluid dynamics simulation, modeling a perfect gas hot jet, counterflowing against a perfect gas supersonic freestream. Plasma effects such as electron pressure, radiation, electric field interactions, Joule heating, and induced vorticity, streamers, and plasmoids have been identified that, if accounted for, may improve the comparison. Procedures for the use of these experimental results have been outlined as a baseline that will be useful in separating fluid dynamic/thermal effects from plasma processes in understanding the physics of onboard plasma jets for aerodynamic augmentation.

Natural motions of sandwich beams with a transversely flexible- (soft-) core are analyzed based on a higher-order theory formulation. The theory does not resort to the use of presumed displacement patterns and permits imposition of the different support conditions at the same boundary section. Finite differences are used to approximate the governing equations, and the deflated iterative Arnoldi algorithm is applied to solve the algebraic eigenvalue problem. Free vibration predictions of the higher-order theory are shown to be in good agreement with experiments reported in the literature. The face sheet deflections of the sandwich beams with nonidentical support conditions at the same boundary are different in the close vicinity of that boundary. The interaction between the face sheets and the core plays a crucial role in the vibration response of sandwich beams with a soft core. The parametric study shows that the qualitative sequence of the antisymmetric (global) and symmetric (local) vibration modes varies with face sheet thickness and that there are sandwich beam layouts for which some higher vibration modes arise from the interaction of the basic modes.

Recent improvements in an unstructured-grid method for large-scale aerodynamic design are presented. Previous work had shown such computations to be prohibitively long in a sequential processing environment. Also, robust adjoint solutions and mesh movement procedures were difficult to realize, particularly for viscous flows. To overcome these limiting factors, a set of design codes based on a discrete ad joint method is extended to a multiprocessor environment using a shared memory approach. A nearly linear speedup is demonstrated, and the consistency of the linearizations is shown to remain valid. The full linearization of the residual is used to precondition the ad joint system, and a significantly improved convergence rate is obtained. A new mesh movement algorithm is implemented, and several advantages over an existing technique are presented. Several design cases are shown for turbulent flows in two and three dimensions.

Thermoelastic equilibrium equations for a functionally graded beam are solved in closed-form to obtain the axial stress distribution. The thermoelastic constants of the beam and the temperature were assumed to vary exponentially through the thickness. The Poisson ratio was held constant. The exponential variation of the elastic constants and the temperature allow exact solution for the plane thermoelasticity equations. A simple Euler-Bernoulli-type beam theory is also developed based on the assumption that plane sections remain plane and normal to the beam axis. The stresses were calculated for cases for which the elastic constants vary in the same manner as the temperature and vice versa. The residual thermal stresses are greatly reduced, when the variation of thermoelastic constants are opposite to that of the temperature distribution. When both elastic constants and temperature increase through the thickness in the same direction, they cause a significant raise in thermal stresses. For the case of nearly uniform temperature along the length of the beam, beam theory is adequate in predicting thermal residual stresses.

A three-node flat triangular element incorporating layerwise zig-zag theory is developed that is suitable for analyzing damped laminated composite structures. By the use of an interdependent kinematic relation, the higher-order shear rotations are replaced by in-plane displacements, a transverse displacement, and section rotations, which result in three translations and two rotations. Natural frequencies and modal loss factors of cantilevered laminated plates with embedded damping layers are calculated with the zig-zag triangular element and compared to the experimental results and MSC/NASTRAN results using a layered combination of plate and solid elements. Frequencies and corresponding loss factors of symmetric and antisymmetric damped laminated cantilever plates as a function of fiber angle are also calculated.

A large eddy simulation (LES) of a turbulent flow past an airfoil near stall at a chord Reynolds number of 2.1 x [10.sup.6] is performed and compared with wind-tunnel experiments. This configuration still constitutes a challenging test case for Reynolds-averaged Navier-Stokes (RANS) simulation and LES as a result of the complexity of the suction side boundary layer: an adverse pressure gradient creates successively a laminar separation bubble, a turbulent reattachment, and a turbulent separation near the trailing edge. To handle this high-Reynolds-number flow with LES on available supercomputers, a local mesh-refinement technique and a discretization of the convective fluxes are developed in a block-structured finite volume code to reduce the total number of grid points and the numerical dissipation acting on the small scales, respectively. Influence of subgrid scale modeling (SGS) is assessed through the comparisons of explicit selective mixed scale model (SMSM) and implicit monotone-integrated LES model results. Moreover, the solution sensitiveness to grid refinement and spanwise extent is investigated. With the use of the largest grid (7.2 x [10.sup.6] cells) and SMSM model, the computed mean and fluctuating velocity profiles compare favorably with experimental measurements, which constitute to the authors' knowledge the first satisfying LES of this complex flow.

Experiments conducted on a flat plate wake in a compressible flow at Mach 2 are described. Large-scale organized motions are revealed both in the separating boundary layer upstream and in the wake downstream. The organized motions in the wake contained within them embeded vortex structures, whose periodicity was found to be weak. The broadband spectra contained a distinct frequency with a Strouhal number of 0.3. The study of mean flow characteristics showed that some qualitative similarity exists in the near- and intermediate-wake regions. The relative Mach number distribution showed the compressibility effects to be small.

We present experimental results on the mean flow development and potential core lengths of single- and dual-stream compressible air jets. The research is relevant to noise emission, thermal signature, and combustion in high-speed turbulent jets. The primary flow was set at Mach number 1.5, and the secondary stream was supplied at four subsonic Mach numbers from nozzles of variable area and shape. Coaxial and eccentric nozzle configurations were investigated. In the coaxial arrangements, the secondary flow reduces the growth rate of the primary shear layer and elongates the primary potential core. As a result, the mass entrainment rate of the coaxial jet is less than that of the single jet. The potential core is stretched by 68% when a secondary stream with area ratio 2.9 is supplied at Mach number 0.9. The eccentric configuration shows substantial improvement in mixing over the coaxial case and achieves an entrainment rate roughly equal to that of the single jet when the exit areas of the primary and secondary streams are approximately equal. On an equal mass flow rate basis, the eccentric dual-stream jet with area ratio 0.9 actually mixes faster than the single jet. The potential core and the supersonic region of the jet are elongated much less than in the coaxial case. A semi-empirical model, based on the present data and classical shear layer relations, is proposed for the primary and secondary core lengths of coaxial jets.

A Newton-Krylov algorithm is presented for two-dimensional Navier-Stokes aerodynamic shape optimization problems. The algorithm is applied to both the discrete-adjoint and the discrete flow-sensitivity methods for calculating the gradient of the objective function. The adjoint and flow-sensitivity equations are solved using a novel preconditioned generalized minimum residual (GMRES) strategy. Together with a complete linearization of the discretized Navier-Stokes and turbulence model equations, this results in an accurate and efficient evaluation of the gradient. Furthermore, fast flow solutions are obtained using the same preconditioned GMRES strategy in conjunction with an inexact Newton approach. The performance of the new algorithm is demonstrated for several design examples, including inverse design, lift-constrained drag minimization, lift enhancement, and maximization of lift-to-drag ratio. In all examples, the norm of the gradient is reduced by several orders of magnitude, indicating that a local minimum has been obtained. By the use of the ad joint method, the gradient is obtained in from one-fifth to one-half of the time required to converge a flow solution.

The fast response time characteristics of porous pressure-sensitive paint (porous PSP) are applied to unsteady flowfield measurements. The unsteady flowfield of a fluidic oscillator is investigated by using anodized aluminum (AA), thin-layer chromatography (TLC), and polymer/ceramic (PC) as porous supporting matrices. The frequency response of these PSPs is measured using a shock tube, showing responses of 12.2, 11.4, and 3.95 kHz for AA-PSP, TLC-PSP, and PC-PSP, respectively. Flow oscillations of various phases are captured with these porous PSPs in the fluidic oscillator tests, with AA-PSP giving the sharpest images.

An analytical model is developed to analyze the effects of viscous flow on residual stresses in film-substrate systems. Compared to viscous flow in the film, viscous flow in the substrate results in slower stress relaxation in the system.

Byline: E. I. Batyr (1) Abstract: The linear hydrodynamic problem involving the small motions and normal oscillations of a double pendulum with cavities completely filled with a liquid is examined. The problem is solved using the methods of functional analysis. An existence theorem is formulated for the solutions to the Cauchy problem and the properties of the normal oscillations are described. Author Affiliation: (1) Taurian National University, Ukraine Article History: Registration Date: 06/10/2004

The bifurcation structure of viscous flow in curved square ducts is studied numerically and the stability of solutions on various solution branches is examined extensively. The solution structure of the flow is determined using the Euler-Newton continuation, the arc-length continuation, and the local parameterization continuation scheme. Test function and branch switch technique are used to monitor the bifurcation points in each continuation step and to switch branches. Up to 6 solution branches are found for the case of a flow in the curved square channel within the parameter range under consideration. Among them, three are new. The flow patterns on various bifurcation branches are also examined. A direct transient calculation is made to determine the stability of various solution branches. The results indicate that, within the scope of the present work, at given set of parameter values, the arbitrary initial disturbances lead all solutions to the same state. In addition to stable steady two-vortex solutions and temporally periodic solutions, intermittent and chaotic oscillations are discovered within a certain region of the parameter space. Temporal intermittency that is periodic for certain time intervals manifests itself by bursts of aperiodic oscillations of finite duration. After the burst, a new periodic phase starts, and so on. The intermittency serves as one of the routes for the onset of chaos. The results show that the chaotic flow in the curved channel develops through the intermittency. The chaotic oscillations appear when the number of bursts becomes large. The calculations also show that transient solutions on various bifurcation branches oscillate chaotically about the common equilibrium states at a high value of the dynamic parameter. [DOI: 10.1115/1.1412457]

A finite-difference scheme is used to solve the Navier-Stokes equations for the steady flow inside and outside viscous spheres in a fluid of different properties. Hence, the hydrodynamic force and the steady-state drag coefficient of the spheres are obtained. The Reynolds numbers of the computations range between 0.5 and 1000 and the viscosity ratio ranges between 0 (inviscid bubble) and infinity (solid particle). Unlike the numerical schemes previously implemented in similar studies (uniform grid in a stretched coordinate system) the present method introduces a two-layer concept for the computational domain outside the sphere. The first layer is a very thin one [0 ([Re.sup.-1/2)]] and is positioned at the interface of the sphere. The second layer is based on an exponential function and covers the rest of the domain. The need for such a double-layered domain arises from the observation that at intermediate and large Reynolds numbers a very thin boundary layer appears at the fluid-fluid interface. The computations yield the friction and the form drag of the sphere. It is found that with the present scheme, one is able to obtain results for the drag coefficient up to 1000 with relatively low computational power. It is also observed that both the Reynolds number and the viscosity ratio play a major role on the value of the hydrodynamic force and the drag coefficient. The results show that, if all other conditions are the same, there is a negligible effect of the density ratio on the drag coefficient of viscous spheres. [DOI: 10.1115/1.1412458]

The computation of viscous flow for a Boeing 777-200 aircraft configured for landing uses a structured overset grid process and computational fluid dynamics techniques.

Local simulations with up to 60,000 self-gravitating dissipatively colliding particles indicate that dense unperturbed ring systems with optical depth [tau] > 1 can exhibit spontaneous viscous oscillatory instability (overstability), with parameter values appropriate for Saturn's B ring. These axisymmetric oscillations, with scale ~100 m and frequency close to the orbital period, generally coexist with inclined Julian-Toomre type wakes forming in gravitating disks. The onset of overstability depends on the internal density of particles, their elasticity, and the size distribution. The same type of oscillatory behavior is also obtained in an approximation where the particle--particle gravity is replaced by an enhanced frequency of vertical oscillations, [[OMEGA].sub.z]/[OMEGA] > 1. This has the advantage that these systems can be more easily studied analytically, as in the absence of wakes the system has a spatially uniform ground state. For [[OMEGA].sub.z]/[OMEGA] = 3.6 overstability again starts at [tau] ~ 1. Also, nongravitating systems, [[OMEGA].sub.z]/ [OMEGA] = 1, show overstability, but this requires [tau] ~ 4. To facilitate a quantitative hydrodynamical study of overstability we have measured the transport coefficients (kinematic shear viscosity [nu], kinematic bulk viscosity [zeta], and kinematic heat conductivity [kappa]) in simulations with [[OMEGA].sub.z]/[OMEGA] = 3.6, 2.0, and 1.0. Both local and nonlocal (collisional) contributions to the momentum and energy flux are taken into account, the latter being dominant in dense systems with large impact frequency. In this limit we find [zeta]/[nu] [approximately equals] 2, [kappa]/[nu] [approximately equals] 4. The dependence of pressure, viscosity, and dissipation on density and kinetic temperature changes is also estimated. Preliminary comparisons indicate that the condition for overstability is [beta] > [[beta].sub.cr] ~ 1, where [beta] := [Delta]log(nu)/[Delta] log(tau]). This limit is clearly larger than the [[beta].sub.cr] ~ 0 suggested by the linear stability analysis in Schmit and Tscharnuter (1995), where the system was assumed to stay isothermal even when perturbed. However, it agrees with the nonisothermal analysis in Spahn et al. (2000). This increased stability is in part due to the inclusion of temperature oscillations in the analysis, and in part due to bulk viscosity exceeding shear viscosity. A detailed comparison between simulations and hydrodynamical analysis is presented in a separate paper (Schmidt et al. 2001).

We investigate the viscous oscillatory instability (overstability) of an unperturbed dense planetary ring, an instability that might play a role in the formation of radial structure in Saturn's B-ring. We generalize existing hydrodynamic models by including the heat flow equation in the analysis and compare our results to the development of overstable modes in local particle simulations. With the heat flow, in addition to the balance equations for mass and momentum, we take into account the balance law for the energy of the random motion; i.e., we allow for a thermal mode in a stability analysis of the stationary Keplerian flow. We also incorporate the effects of nonlocal transport of momentum and energy on the stability of the ring. In a companion paper (Salo, H., J. Schmidt, and F. Spahn 2001. Icarus, doi:10.1006/icar.2001.6680) we describe the determination of the local and nonlocal parts of the viscosity, the heat conductivity, the pressure, as well as the collisional cooling, together with their dependences on temperature and density, in local event-driven simulations of a planetary ring. The ring's self-gravity is taken into account in these simulations by an enhancement of the frequency of vertical oscillations [[OMEGA].subs.z] > [OMEGA]. We use these values as parameters in our hydrodynamic model for the comparison to overstability in simulated rings of meter-sized inelastic particles of large optical depth with [[OMEGA].sub.z]/[OMEGA] = 3.6. We find that the inclusion of the energy-balance equation has a stabilizing influence on the overstable modes, shifting the stability boundary to higher optical depths, and moderating the growth rates of the instability, as compared to a purely isothermal treatment. The non-isothermal model predicts correctly the growth rates and oscillation frequencies of overstable modes in the simulations, as well as the phase shifts and relative amplitudes of the perturbations in density and radial and tangential velocity. Key Words: planetary rings; Saturn.

Byline: I. T. Selezov (1), O. V. Zvonareva (1) Abstract: The propagation of waves generated by pressure pulses in a cylindrical elastic shell filled with a viscous fluid is investigated. The problem models the propagation of a pulse pressure wave in a blood vessel and is solved by means of Laplace transforms. This approach permits analytical solutions to be constructed in transform space. The original functions are recovered by numerical inversion of the Laplace transform. The results are analyzed for various values of the parameters. Author Affiliation: (1) National Academy of Sciences of Ukraine, Ukraine Article History: Registration Date: 06/10/2004

We examine the local dynamics of nonisothermal viscous flows in the neighborhood of the constant equilibria using the thermomechanically consistent constrained theory for materials with prescribed temperature-dependent density developed by Cao et al., We discover that the linearized growth rate of small length scale, infinitesimal disturbances near the equilibria is proportional to the reciprocal of their wave length, a classical phenomenon known as the Hadamard instability, indicating the local ill-posedness of the constrained theory. Therefore, the use of the theory to model transient flow phenomenon is not advised. [S0021-8936(00)01901-2]

Nusselt numbers in rectangular ducts with laminar viscous dissipation have been analytically determined for a Newtonian incompressible fluid for any combination of heated and adiabatic duct sides. That the temperature field in a fully developed T boundary condition can be obtained as a particular case of the H1 problem and that the corresponding Nusself numbers do not depend on the Brinkman number has been proved.

Viscous liquid flows and their enhanced heat transfer characteristics in a chevron plate heat exchanger are discussed. Vegetable oil was used as the test fluid with three plate arrangements. A rather complex influence of plate surface corrugations was found on the enhanced thermal-hydraulic behavior.

Transporting heavy crude oil by pipeline requires special facilities because the viscosity is so high at normal field temperatures. In some cases the oil is heated with special heaters along the way, while in others the oil may be diluted by as much as 30 percent with kerosene. Commercial drag reducers have not been found to be effective because the single-phase flow is usually laminar to only slightly turbulent. In this work we show the effective viscosity of heavy oils in pipeline flow can be reduced by a factor of 3-4. It is hypothesized that a liquid crystal microstructure can be formed so that thick oil layers slip on thin water layers in the stress field generated by pipeline flow. Experiments in a 1 1/4-in. flow loop with Kern River crude oil and a Venezuela crude oil BCF13 are consistent with this hypothesis. The effect has also been demonstrated under field conditions in a 6-in. flow loop using a mixture of North Sea and Mississippi heavy crude oils containing 10 percent brine.

Gravity-driven flow over a round-crested weir is analyzed for viscous flow. An equation for the entire flow profile is obtained by simplifying the equations for slowly varying film thickness, assuming a velocity profile, and integrating across the film. Solution of the resulting first order, ordinary differential equation requires a boundary condition generated at a critical point of the flow, beyond which waves cannot propagate upstream. Results for the relationship between head and flow rate are consolidated on a dimensionless master curve represented by an empirical equation.

The use of 3M riblets on reducing viscous drag on a swept wing with a general aviation wing airfoil section at low speeds has been assessed. The surface-pressure distributions, total drag, mean velocity, turbulence intensity and Reynold shear-stress profiles were measured at a chord Reynolds number of 0.75 X 10 raised to the 6th power, at an incidence range of 0 to 6 deg. Results indicate maximum and total viscous drag reductions of 6 and 8%, respectively, at zero incidence. These results are comparable to those obtained on two-dimensional flat plates and airfoils.

To introduce the intermittency effects of the energy cascade process into turbulence modeling, a new fractal turbulence scale based on k, [Epsilon], v, and the fractal dimension of turbulence dissipation D, with D = 2.7, is introduced, and a fractal scale, low Reynolds number turbulence model is proposed. The proposed turbulence model is first examined in detail by predicting a two-dimensional channel flow, and then applied to predict a backward-facing step flow. Numerical results are compared with the direct numerical simulation budgets, experimental data, and the model results of Chien, and Lam and Bremhorst, respectively. It is found that the fractal scale model indeed predicts better results for both of the flows considered.

The present work demonstrates that the assumption of wall similarity in the equilibrium region of open channels leads to the definition of a constant, universal value for the normalized vertical flux of turbulent kinetic energy irrespective of wall roughness. Moreover, by additionally assuming a gradient-flux model for the turbulent kinetic energy, its bed-normal distribution is easily estimated by an expression with parameters that rely on a physical basis. Turbulence measurements performed in smooth-, transitionally rough-, and fully rough-bed (sandgrain) open channels confirm this hypothesis, providing at the same time an alternative way of determining the lower and upper limits of the intermediate region. Finally, based upon wall-similarity assumptions, a new methodology is proposed for estimating mean bed-shear velocities (stresses) in free-surface flows at high local and global Reynolds numbers, irrespective of roughness condition at the bed.

A combined experimental and computational study was carried out to investigate the laminar flow of a nonlinear viscoplastic fluid through an axisymmetric sudden expansion. The yield-stress, power-law index, and the consistency index of the yield shear-thinning test fluid were 0.733 Pa, 0.68, and 0.33 Pa [multiplied by] [s.sup.0.68], respectively, resulting in a Hedstrom number of 1.65. The Reynolds number ranged between 1.8 and 58.7. In addition, the flow of a Newtonian fluid through the same expansion was also studied to form a baseline for comparison. Velocity vectors were obtained on the vertical center plane using a digital particle image velocimeter (PIV). From these measurements, two-dimensional distributions of axial and radial velocity as well as the stream function were calculated covering the separated, reattached and redeveloping flow regions. These results were compared to finite difference numerical solutions of the governing continuity and fully-elliptic momentum equations. The calculations were found to be in good agreement with the experimental results. Both computational and experimental results indicate the existence of two distinct flow regimes. For low Reynolds numbers, a region of nonmoving fluid is observed immediately downstream of the step and no separated flow zone exists. For the higher Reynolds numbers, a recirculating flow zone forms downstream of the expansion step, which is followed by a zone of stagnant fluid adjacent to pipe wall characterizing reattachment.

We present a second-order accurate finite difference method for numerical solution of the incompressible Navier-Stokes equations in deforming domains. Our approach is a generalization of the Bell-Colella-Glaz predictor-corrector method for incompressible flow. In order to treat the time-dependence and inhomogeneities in the incompressibility constraint introduced by presence of deforming boundaries, we introduce a nontrivial splitting of the velocity field into vortical and potential components to eliminate the inhomogeneous terms in the constraint and a generalization of the Bell-Colella-Glaz algorithm to treat time-dependent constraints. The method is second-order accurate in space and time, has a time step constraint determined by the advective Colella-Friedrichs-Lewy condition, and requires the solution of well behaved linear systems amenable to the use of fast iterative methods. We demonstrate the method on the specific example of viscous incompressible flow in an axisymmetric deforming tube.